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Arlon
Online Engineering
Library - TechRef!
Trigonometry
Trigonometric functions are defined using a right triangle.
sin  = y/r, cos = x/r
tan = y/x, cot = x/y
csc = r/y, sec = r/x |
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Law of Sines
a/(sin A) = b/(sin B) = c/(sin C)
Law of Cosines
a2 = b2 + c2 - 2bc cos A
b2 = a2 + c2 - 2ac cos B
c2 = a2 + b2 - 2ab cos C
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Identities
csc = 1/sin
sec = 1/cos
tan = sin /cos
cot = 1/tan
sin2 + cos2 = 1
tan2 + 1 = sec2
cot2 + 1 = csc2
sin ( +  ) = sin cos + cos sin
cos ( + ) = cos cos - sin sin
tan ( + ) = (tan + tan )/(1 - tan tan )
cot ( + ) = (cot cot - 1)/(cot + cot )
sin ( - ) = sin cos - cos sin
cos ( - ) = cos cos + sin sin
tan ( - ) = (tan - tan )/(1 + tan tan )
cot ( - ) = (cot cot + 1)/(cot - cot )
sin 2 = 2 sin cos
cos 2 = cos2 - sin2 = 1 - 2 sin2 = 2 cos2 - 1
tan 2 = (2 tan )/(1 - tan2)
cot 2 = (cot2 - 1)/(2 cot )
sin (/2) = ± 
cos (/2) = ± 
tan (/2) = ± 
cot (/2) = ± 
sin sin = (1/2)[cos ( - ) - cos ( + )]
cos cos = (1/2)[cos ( - ) + cos ( + )]
sin cos = (1/2)[sin ( + ) + sin ( - )]
sin + sin = 2 sin (1/2)( + ) cos (1/2)( - )
sin - sin = 2 cos (1/2)( + ) sin (1/2)( - )
cos + cos = 2 cos (1/2)( + ) cos (1/2)( - )
cos - cos = -2 sin (1/2)( + ) sin (1/2)( - )
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